Asymptotic Stability of Port-Hamiltonian Systems

We characterise asymptotic stability of port-Hamiltonian systems by means of matrix conditions using well-known resolvent criteria from \(C_0\) -semigroup theory. The idea of proof is based on a recent characterisation of exponential stability established in Trostorff and Waurick (Characterisation for Exponential Stability of port-Hamiltonian Systems, 2024), which was inspired by a structural observation concerning port-Hamiltonian systems from Picard et al. (SIAM J Control Optim 61(2):511–535, 2023). We apply the result to study the asymptotic stability of a network of vibrating strings.